Adding and Subtracting Fractions
w/ 21+ Examples!

What are the rules for adding and subtracting fractions?

Great question!

That’s exactly what you’re going to learn in today’s math lesson!

After the lesson you’ll have the knowledge to tackle fractions with like and unlike denominators with ease.

In addition, you’ll be able to practice your skills with the worksheets below.

But what do you do when drawing a picture isn’t feasible?

You use the steps for how we add and subtract fractions!

With Like Denominators

First, you check to see if the fractions have the same denominators.

If the fractions do have the common denominators, then you keep the denominator and add or subtract the numerators.

Example #1

Find the sum of 3/5 and 1/5.

Example #2

Find the difference between 7/12 and 2/12.

With Unlike Denominators

If the fractions have different denominators, then you’ll complete these 3 initial steps.

1. Find the Least Common Denominator (LCD).
2. Convert each fraction to an equivalent fraction with the LCD as the new denominator.
3. Then you will add or subtract the numerators while keeping the new common denominator the same as discussed on The Math Page.

Remember, when determining the LCD, all we have to do is find the least common multiple (LCM)!

Example #1

Find the difference between 2/3 and 5/9.

Example #2

Find the sum of 1/2 and 2/3.

Then, you will reduce the resulting sum or difference to the lowest terms by dividing the numerator and denominator by the greatest common factor (GCF).

And finally, if necessary, you will convert improper fractions to whole or mixed numbers.

Let’s look at a few more problems.

Example #3

Find the sum of 1/2 and 3/10.

Example #4

Find the difference between 10/3 and 9/5.

Adding And Subtracting Mixed Fractions

But there are many times when we are asked to add or subtract mixed numbers and improper fractions.

Whenever this happens, you must first transform the mixed number into an improper fraction or the improper fraction into a mixed number.

Personally, I find that changing mixed numbers to improper fractions is always easier!

And then, we follow the steps outlined above.

Example #1

Find the sum of 1 and 1/8 and 7/6.

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

Adding and Subtracting Fractions — Practice Problems
Adding and Subtracting Fractions — Step-by-Step Solutions

Final Thoughts

Throughout the video lesson below, you’ll learn:

• The rules for adding and subtracting fractions on more advanced problems.
• How to find the LCD, which is nothing more than finding the LCM, to create common denominators.
• The process to add mixed numbers, whole numbers, improper fractions, and even how to handle three fractions at one time.

It’s a fun process when you understand the fundamentals!

Let’s go!

Video Tutorial — Full Lesson w/ Detailed Examples

1 hr 35 min

• Introduction to Video
• 00:00:45 – How do you work with fractions?

• 00:05:06 – Fractions with common denominators and reduce to simplest terms (Examples #1-4)
• 00:13:24 – Using fractions with uncommon denominators and simplify results (Examples #5-8)
• 00:31:36 – Solve two or more fractions and reduce to lowest terms(Examples #9-12)
• 00:52:02 – Calculate the mixed numbers and simplify results (Examples #13-16)
• 01:08:05 – Add or subtract fractions and whole numbers and reduce to simplest terms (Examples #17-18)
• 01:16:18 – Addition and Subtraction for three fractions as indicated and reduce to lowest terms (Example #19)
• 01:22:26 – Solve three fractions and leave in simplest terms (Examples #20-21)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions